It is also the largest integer which cannot be written as a sum of 32, 33, 34 or 35 nonnegative fifth powers; there are only fifteen, ten, six and three nonnegative integers with this property, respectively.

It is also the number of matches in the association football Czech First League, which has a 16-team double round-robin tournament, and the association football Israeli Premier League, which has a 14-team double round-robin tournament followed by a six-team double round-robin tournament and an eight-team single round-robin tournament.

Furthermore, it was the number of pre-decimal pence in a pound sterling.

In the association football Danish Superliga, there are 14 teams playing a double round-robin tournament followed by a six-team double round-robin tournament and two four-team double round-robin tournaments, seven two-legged play-off ties, and a single-legged play-off tie, resulting in 251 matches.

It is also the number of species in the first two Pokémon generations.

360 is the order of the alternating group of degree 6, which is isomorphic to the matrix group PSL(2,9), and to B2(2)′. It is one of the few non-abelian simple groups with only three distinct prime factors in the order.

It is also the number of seats in the 14th Bundestag, which was until 2017 the largest democratically elected national parliament house ever.

The 19th Bundestag is the largest democratically elected national parliament house ever; it has 709 seats.

A method for generating a sequence of primes is to start with 1, then choosing the smallest prime successor of a multiple of the previous number in each step. The compositeness can be easily certified by Fermat or Miller-Rabin, and the primality by Pratt. The resulting sequence starts with 1, 2, 3, 7, 29, 59, 709, … (OEIS A061092).